Hensley D. — Continued Fractions :: Электронная библиотека попечительского совета мехмата МГУ

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Hensley D. — Continued Fractions

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Название: Continued Fractions

Автор: Hensley D.

Аннотация:

This book places special emphasis on continued fraction Cantor sets and the Hausdorff dimension, algorithms and analysis of algorithms, and multi-dimensional algorithms for simultaneous diophantine approximation. Extensive computer-generated graphics are presented, and the underlying algorithms are discussed and made available.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2006

Количество страниц: 245

Добавлена в каталог: 13.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Absolutely continuous      79 86
Algebraic extension      125 126
Algebraic integer      26 28 29 126 127 129 137 141—143
Algebraic integer-quartic      82
Algebraic number      24 100 125 127 136
Algorithm      1 2 7 11 31 34 36 41 44 45 150
Algorithm, Gauss      102
Algorithm, Jacobi — Perron      127
Algorithm, LLL      29 103 116
Algorithm, Pincke — Pohst      115 116
Algorithm-CF      61
Algorithm-Euclidean      3
Algorithm-Lagarias      128
Analytic continued fraction      224
Approximation error      8 70 71 75 127
Approximation error-best possible      14 104
Approximation error-normalized      49
Approximation-simultaneous      101
Askey      185 188
Astels      145 151
Babenko      181
Badly approximable      143
Badly approximable vector      18 100 125 127 128
Baladi      209
Banach space      54 87 162 167 207
Bandtlow      87
Basis, lattice      29 102
Basis, reduced      102
Bessel function      184 230
Binary shift      3
Bohmer      19
Borel set      215
Borosh      154
Bosma      49
Bounded distortion property      213
Bounded linear operator      90 186
Bounded partial quotients      33 34 37 39 45 46 161
Bridge      145 150
Burger      21
Cantor set      145 213
Cassels      100
Cauchy — Schwarz inequality      182 185 199
Cauchy’s inequality      89
Centered continued fraction      40 41 72 206
CF algorithm      61
Clarke      230
Cohen      28
Cohn, H.      19
Compact operator      87 90 91 169 170 189
Compact operator, s-numbers of      170
Compact set      177
conformal      93 94
Conjugates-of an algebraic number      134
Continuant      6 76
Continued fraction algorithm-Hurwitz      71
Continued fraction Cantor set      36 145 161 163
Continued fraction expansion      225 229—231
Continued fraction expansion-      71
Continued fraction expansion-for log(l + z)      230
Continued fraction expansion-of       228
Continued fraction expansion-tanh(z)      225
Continued fraction expansion-unusual      19 20 82
Continued fraction, expansions-miscellaneous      230
Continued fraction-analytic      225
Continued fraction-convergent      10—12 14 17 21 24
Continued fraction-nonconvergence of      218
Continued fraction-periodic      8 9
Continued fraction-purely periodic      9 10
Continued fraction-rewriting      218
Continued fraction-terminating      8
Convergent      14 72 75 218 225 231
Convex polytope      125
Convex set      117 119
Convex-polyhedron      119
Correspondence-of a continued fraction to a function      225
Cusick      153 164
Cylinder      134
Daude      31
Degree-of a field extension      133
Degree-of a polynomial      24 26
Degree-of an algebraic number      127 129 131 133—138 140 141
Delange      208
Determinant      6 101 113 118 119
Determinant-of a lattice      21 104
Dimension-of a lattice      102
Diophantine approximation      13 100 102 111
Dirichlet pigeonhole principle      127
Dirichlet series      209
Discrepancy      13 18 39 45 46
Discrete spectrum      208
Divis      151
Dominant eigenvalue      92 156 166
Doubling property      216
Doubling property-of a measure      215
Drmota      100 127
Dynamical system      50—52 205
Dynamical system-extension      58
Eigenfunction      53 206 215
Eigenfunction-dominant      32
Eigenfunction-positive      208
Eigenvalue-dominant      53 215
ellipse      128
Encyclopedia of Integer Sequences      44
entropy      206
Ergodic      49—51 57 63 155 206
Euclid      1
Euclidean algorithm      1 3 4 7 30 103
Euclidean algorithm-binary      3
Euclidean algorithm-centered      3
Euclidean algorithm-extended      4
Euclidean Domain      23 24
Euler      5
Field-algebraic      28
Field-extension      29
Fincke — Pohst algorithm      31 115
Finite field      5 7 24 25 33
Flahive      153
Flajolet      31 190
Folding lemma      20
Fractal      46 81 163
Fractal set      214
Fractal string      166
Frankenhuysen      166
Freiman      152
Friesen      5 26
Fundamental set of units      132
Fundamental unit-of an algebraic number field      129
Gauss      102 108 155
Gauss density      79 158
Gauss measure      51 56
Gauss — Kuz’min theorem      73 79 156 157
Gaussian (normal) distribution      2 209
Gaussian integer      23 26 27 30 67 74 77 80 94
GCD      1 2 4 7 13 26 28 113 118 119
gcd-of ideals      29
Generating function      207
Geodesic      106
Geometric zeta function      166
Golden mean      19
Good denominator      127 129 132 135—137 139 143
Good unit      133—137
Gram — Schmidt algorithm      102 103
Grothendieck      189
Group      4 29 222
Group-generator      4
hadamard      12
Hall      145
Halton sequence      46
Hammersley sequence      46
Harman      21

Hausdorff dimension      36 37 100 163—166 174 214 215
Hensley’s constant      210
hermite      32 105 107
Hermite approximation      107
Hermite denominator      32 107 108 111—115 125 128
Hilbert space      168 181 189
Holomorphic      207
Holomorphic function      90
Hurwitz algorithm      71 72 79 80
Hurwitz, A.      8 72
Hurwitz, J.      74
Hyperbola      129
Hyperbolic tangent      225
Hypergeometric function      227
Ideal      28 29
Ideal-finitely generated      29
Individual ergodic theorem      51 52
Integral basis      29
Integral basis-of an ideal      29
Invariant density      79 86 155 206
Invariant measure      56
Invariant subspace      208
Inverse branch      205
Iterated function system      213 214
jacobi      101 229
Jacobi symbol      4
Jacobi — Perron algorithm      101 127
Jager      49
Jenkinson      87 175
Jones      217 224
Kessenbohmer      176
Kmosek      19
Knopfmacher      61
Krasnoselskii      87 167
Krasnoselskii generalization      176 177 179
Kronecker algorithm      4
Lagarias      119
Lagarias geodesic algorithm      67 128
Lagrange      13
Lagrange spectrum      145 153
Laguerre polynomial      182 184 186
Laguerre polynomial-generalized      185
Lange      221—223
Lapidus      166
Laplace      155 229
Lattice      21 30 34 102 132
Lattice basis      29 102 103 108
Lattice determinant      104
Lattice reduction      21 28 29 31 32 102—104 108
Lattice reduction-Gaussian      31
Laurent series      225
Lebesgue measure      79 86 100 161 166
legendre      4
Legendre polynomial      230
Lenstra, A.      103
Lenstra, H.      12 49 50 103
Levy metric      177
Lhote      204 210
Linear fractional      94 95 110 205 207 221
Linear functional      54
Linear operator      53 156 162 207 210
LLL algorithm      29 31 103
LLL reduction      102 103
LLL-reduced      103 104
Log convexity      195
Log convexity-strict      202
Lovasz      103
Markoff spectrum      145 153
Markoff triple      154
Mathematica      1 2 185 219 222
Mauldin      175 213—216
Mayer      170
Meromorphic      222
Minkowski dimension      163 166
Minkowski reduced      108 112—114 116 118
Minkowski reduction      28 102
Minkowski-reduced, forward-reduced      114—116 118
Minkowski-reduced, lexicographic      114
Minkowski’s theorem      104
Mixing      51 57 59—61 87
Modular inverse      5
Modular tiling      105
Montel’s theorem      91
Nair      50 51
Niederreiter      25 33 34 36 46
Niederreiter net      46
NP-hard      31 115 125
Nuclear of order zero      186 208
Null space      179 180 208
Ordered derivation      149
Orthogonal set-of eigenvectors      189
Orthogonal vectors      30
Orthonormal set      64 170
Pade approximation      228 229
Parabola theorem      224
PARI      158
Partial quotient      7 11 17 111 217
Partition-of C      67
Pell’s equation      10 11
Perron      101 217 227—229
Perron — Frobenius theorem      87 167 176
Perturbation theory      208
Pigeonhole Principle      127
Pisot — Vijayaraghavan number      26 131
Point spectrum      189
Polynomial-primitive      25
Porous-fractal set      214
Positive cone      92
Positive operator      87 156 176 208
Positive, -positive      87 176
Pressure function      214
Prime-sum of two squares      20
Principal ideal domain      30
probability density      79 87 155 156 158 206
Projection      87 180 215
Proper cone      176
Pseudo-random numbers      25 34
pseudorandom      82
Quadratic irrational      8 9 12 18
Quadratic nonresidue      20 31
Quadratic residue      4
Random number      155
Random walk      18
Reduced basis      28 102
Regular chain      67 68
Relatively prime      5
Reproducing cone      176
Restricted partial quotients      50
Riemann sum      56
Riesz representation theorem      179
Rohlin      206
Rohlin’s formula      206
Saff      229
Sander      36
Scaled error      82 83 85 127 130 139 142
Scaled error-typical      49
Schmidt, A.      27 67 72
Schmidt, W.      100
Schoibengeier      46
Seidel      229
Shallit      12 19
Sierpinski gasket      100
Signature-of a field extension      132 133
Signature-of an algebraic number      138 141
Simultaneous diophantine, approximation      32 101
Sloane      44
smith      19
Spectral gap      167 198
Spectral gap-uniform      190
Spectral radius      32 87 163 165 208

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